Ant Colony Optimization By: Aaron Obernuefemann October 22 nd , 2012 Data Mining Methods MATH 3220
Overview • Definition of Ant Colony Optimization (ACO) • Terminology • Metaheuristics • The Algorithm • ACO Example • Summary • References
Definition • Ant colony optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. • (ACO) studies artificial systems that take inspiration from the behavior of real ant colonies
Terminology • Pheromones- markers • Combinatorial Optimization (CO)- a topic that consists of finding an optimal object from a finite set of objects • Computational Complexity- A mathematical characterization of the difficulty of a mathematical problem which describes the resources required by a computing machine to solve the problem • Heuristic- pertaining to a trial-and-error method of problem solving used when an algorithmic approach is impractical
Metaheuristics • Guides other heuristics to search for solutions in domains • Generally applied to problems classified as NP-Hard or NP-Complete by the theory of computational complexity • Also applied to other combinatorial optimization problems
The Algorithm • proposed by Marco Dorigo in 1992 • a member in swarm intelligence methods and it constitutes some metaheuristic optimizations • a probabilistic technique for solving computational problems which can be reduced to finding good paths
Picture Source: Wikipedia F = Food ; N = Nest
ACO Example: Traveling Sales Problem • Marco Dorigo described in 1997 a method of heuristically generating "good solutions" to the TSP using a simulation of an ant colony system called ACS (Ant Colony System) • It models behavior observed in real ants to find short paths between food sources and their nest • Each ant probabilistically chooses the next city to visit based on a heuristic combining the distance to the city and the amount of virtual pheromone deposited on the edge to the city. • The amount of pheromone deposited is inversely proportional to the tour length: the shorter the tour, the more it deposits.
• sends out a large number of virtual ant agents to explore many possible routes on the map • the ants explore, depositing pheromone on each edge that they cross, until they have all completed a tour • the ant which completed the shortest tour deposits virtual pheromone along its complete tour route ( global trail updating )
Summary • Defined ACO • Metaheuristics • The Algorithm • Traveling Sales Problem
References • "Ant Colony Optimization." - Scholarpedia . N.p., n.d. Web. 11 Oct. 2012. <http://www.scholarpedia.org/article/Ant_colony_optimization>. • "Metaheuristic." Dictionary.com . Dictionary.com, n.d. Web. 12 Oct. 2012. <http://dictionary.reference.com/browse/metaheuristic>. • "Tabu Search." Reference.com . N.p., n.d. Web. 12 Oct. 2012. <http://www.reference.com/browse/Tabu_search>. • "Ant Colony Optimization Algorithms." Wikipedia . Wikimedia Foundation, 3 Apr. 2010. Web. 15 Oct. 2012. <http://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms>. • "Travelling Salesman Problem." Wikipedia . Wikimedia Foundation, 10 Jan. 2011. Web. 18 Oct. 2012. <http://en.wikipedia.org/wiki/Travelling_salesman_problem>. • http://dictionary.reference.com/browse/heuristic?s=t
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